As we have continually worked on factor pairs throughout the year, I have seen students become more fluent in being able to list them systematically. 72 is a demanding product to list factor pairs for. They struggled. But through this struggle, the fluidity improves and their fact knowledge takes on a different and more advanced meaning than just memorizing facts. I like this standard very much and can see how useful it is!

To warm up today we worked on finding our factor pairs from 69-75. This continues to help us achieve standard 4.OA. B.4 Factor Pairs 69-72. This photo shows a student using a factor pair calculator to check to see if the number was prime.

I listed the numbers on my whiteboard and asked students to recall what listing strategies we have learned to easily find factor pairs.

Various students responded:

1. Start to list the factor pairs starting with 1x the product.

2. Use divisibility rules: If it's even, divide by 2. If the digits add up to a number that is divisible by 3, then it will divide by 3. It's divisible by 5 if the number ends in a zero or a 5. 10's have zeros on the end. ( I asked them which numbers they know are divisible by 2, 3, 5 and 10 right now just by using their rules.)

4.Stop at the "turn around" ( commutative pair) or decide if it probably is prime. I asked them to tell me what 'prime" means to review.They knew! They all agreed that a prime number has only one factor pair.

We divided up the class and part found 69-72 and the other part found factor pairs for 72-75.I gave both groups 72 because I wanted them to see that 72 has 6 factor pairs....That is one of the higher amounts of factor pairs we have found yet!

Students came up to the board one by one and they listed the factor pairs on the board. We discussed different factors, reviewed what the commutative pairs were and marveled at how many factor pairs 72 has!

Resources (1)

Resources

I directly instructed this lesson today with a comparison of one step and two step word problems that are very similar, using this Comparing Multi-Step Word Problems to One Step SB file. I did this because students who are struggling with multi-step word problems as well as my advanced students need to examine the differences in the wording between the two types of problems. Common Core demands this type of rigorous work and thinking. I have seen students give up in the past prior to Common Core because they had no supportive resources to tap on to organize their thinking and develop their conceptual understanding.It is my hope that this lesson provides the in depth support they need. I followed my SB lesson exactly.

Solving Word Problems Class Notes shows how a rich discussion helped students work hard to understand the differences. The hardest thing for me to get them to understand was why we need to create equations and solve from the equations! As this lesson progressed, we finally find the equation together: Getting There!

*I sent the class notes to them in their emails so they were there for them to refer to as they solved their word problems.

After the whole class lesson, I partnered students that are below grade level achieving with at and above grade level achievers because I wanted students to really engage in a strategy methods conversation. Mixing these levels helps both groups with deepening their understanding of their own learning.

I gave my partnered students enough time to solve two problems from the SB file. I roved the class and saw that they were working hard and dialogue was about setting up the KWS chart as we did in class. I noticed that equations were being formulated correctly with variables. It seemed that they were well on their way and would be able to independently solve the rest at home.

I stopped them for closure by returning to the SB file and used the third and fourth pages.

Embedded in SB File in the picture of the cat is a cute video of a cat chasing a laser beam. I used the analogy between a cat not able to catch the laser light, compared to NOT using strategies. Solving problems without strategies is like chasing things we can't really catch. I wanted to drive the point home that there is no success in solving unless strategies in thinking and solving are used. So, for my closure, I used the last two pages of the SB file. They thought the cat video was hysterical.

I asked them to create an analogy in their math notebooks to compare the cat with them not using strategies and equations. I talked as the video played. I said: "How is the cat like us when we don't use strategies? As we try to solve word problems without a plan, or without thought...it's like spinning and spinning around and never getting what we want...a solution!"

Below is a sample of one of my student's writing responses. An Analogy.

I assigned the rest of the problems for homework by printing a copy of the assignment directly from the SB file.